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1
Preheat the oven to 450.
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2
On a rimmed baking sheet, toss the rye bread pieces with 2 tablespoons of the olive oil and season with salt and pepper.
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3
Bake for about 5 minutes, until the crumbs are light golden but not completely dry.
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4
In a large skillet, heat 2 tablespoons of the olive oil until shimmering.
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5
Add the mushrooms, baking powder and 1/2 teaspoon of the thyme and season with salt and pepper.
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6
Cook over moderately high heat, stirring occasionally, until the mushrooms are tender and browned, about 8 minutes.
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7
Transfer the mushrooms to a plate.
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8
Wipe out the skillet.
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9
Add the remaining 1/4 cup of olive oil and heat until shimmering.
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10
Add the onion, garlic, crushed red pepper and the remaining 1/2 teaspoon of chopped thyme.
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11
Cook over moderate heat, stirring occasionally, until softened and just starting to brown, about 8 minutes.
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12
Add the sausage pieces and cook over moderately high heat, breaking up the meat with a spoon, until browned, about 7 minutes.
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13
Stir in the rye bread crumbs, mushrooms and 1/2 cup of water and season with salt and pepper.
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14
Keep the hash warm over very low heat, stirring occasionally.
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15
Meanwhile, bring a very large, deep skillet of water to a simmer over moderate heat.
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16
Crack the eggs one at a time into a small bowl and carefully add to the simmering water.
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17
Poach the eggs over moderate heat until the whites are set but the yolks are still slightly runny, about 5 minutes.
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18
Using a slotted spoon, carefully lift the poached eggs out of the water; blot them dry with paper towels.
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19
Spoon the hash onto 4 plates and top with the eggs.
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20
Garnish the hash with fleur de sel and snipped chives and serve with hot sauce.
